Abstract
This paper deals with the problem of approximate point set pattern matching in 2D. Given a set P of n points, called sample set, and a query set Q of k points (k ≤ n), the problem is to find a match of Q with a subset of P under rigid motion (rotation and/or translation) transformation such that each point in Q lies in the ε-neighborhood of a point in P. The ε-neighborhood region of a point p i ∈ P is an axis-parallel square having each side of length ε and p i at its centroid. We assume that the point set is well-seperated in the sense that for a given ε> 0, each pair of points p, p′ ∈ P satisfy at least one of the following two conditions (i) |x(p) − x(p′)| ≥ ε, and (ii) |y(p) − y(p′)| ≥ 3ε, and we propose an algorithm for the approximate matching that can find a match (if it exists) under rigid motion in O(n 2 k 2(klogk + logn)) time. If only translation is considered then the existence of a match can be tested in O(n k 2 logn) time. The salient feature of our algorithm for the rigid motion and translation is that it avoids the use of intersection of high degree curves.
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Bishnu, A., Das, S., Nandy, S.C., Bhattacharya, B.B. (2010). A Simple Algorithm for Approximate Partial Point Set Pattern Matching under Rigid Motion. In: Rahman, M.S., Fujita, S. (eds) WALCOM: Algorithms and Computation. WALCOM 2010. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11440-3_10
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DOI: https://doi.org/10.1007/978-3-642-11440-3_10
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